Disclaimer: I have never done or inquired about such a project.
At the risk of stating the obvious, this is a huge undertaking ($$$$) - and a bigger expense the bigger the pool is. It is rare that reno projects do not go over the quoted price (although perhaps some companies can stay on budget).
As a complete DIY job, beyond my expertise. I would contract out the stuff I could not do.
If your pool has recently been in use and has the fence in place, then this is likely not an issue. Its size, however, may still be a factor - especially if you wish to remove the fence. Additionally, it no longer will function as a (human) swimming pool, but will be used to house "livestock." It no longer will contain "swimming pool" water, but "fish" water. This may or may not make a difference from an environmental perspective. If you are running anything electrical to the pool area, this may need to be approved for use. Check with the authorities. Buddy next door may have a DIY pond, but he may not have realized he needed a permit (or chose to ignore the rules). On the other hand, a reputable company doing the work will see that the proper paperwork is in place before going ahead.
I would need to do plenty of homework on that one - equipment AND labour guarantees/warranties, follow-up care, reputation - before committing to a contract with any particular company. Apart from the direct "aquarium" equipment involved, I would imagine there to be considerable work needed in terms of landscaping, etc. so that it looks like a pond and not simply a swimming pool with fishes. Depending on where you live, you may require a permit to own and operate a pond in a residential area. Certain rules, restrictions and obligations may apply. One, generally, cannot have an open body of water on their property without some safety features in place.
Example: I once lived on a two-acre property that had an in-ground pool which had been filled in with soil by a previous owner (to use as a garden). I inquired about removing the dirt and re-establishing a functioning swimming pool. For community safety reasons, an 8-foot fence would have to be constructed to enclose the pool completely, with a gate that locks.
Lastly, consult your home insurance company regarding liability. What if the neighbour's cat goes fishing for lunch, falls in, and drowns? Sounds bizarre, but as a chlorinated swimming pool, animals are less likely to visit. With tempting "livestock" available, it could be a different matter to the insurance company.
Best of luck. Would be great to see some "before and after photos" if you decide to go ahead.